# QM: The Dilation operator

1. Nov 24, 2011

### Keyoke

1. The problem statement, all variables and given/known data

Concicer the dilation operator

$D = \vec{r} * \vec{p}$

Compute $[D,\vec{r} ] and [D, \vec{p}]$

2. Relevant equations

$p = - i * hbar$

3. The attempt at a solution
I think the question is really if $[D, \vec{r}]$ commutes

I got this:
$D = \vec{r} * \vec{p}$
$D = x p_x + y p_y + z p_z$

for the x direction:

$[D, r] = [D, x] = [x, x p_x]$

where do i take it from here?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 24, 2011

### dextercioby

You have absolutely no idea ?? Pick up your book and find those brackets (called <commutator>) and the properties they have.